The Central Role of the Identifying Assumption in Population Size Estimation

Abstract

The problem of estimating the size of a population based on a subset of individuals observed across multiple data sources is often referred to as capture-recapture or multiple-systems estimation. This is fundamentally a missing data problem, where the number of unobserved individuals represents the missing data. As with any missing data problem, multiple-systems estimation requires users to make an untestable identifying assumption in order to estimate the population size from the observed data.Approaches to multiple-systems estimation often do not emphasize the role of the identifying assumption during model specification, which makes it difficult to decouple the specification of the model for the observed data from the identifying assumption. We present a re-framing of the multiple-systems estimation problem that decouples the specification of the observed-data model from the identifying assumptions, and discuss how log-linear models and the associated no-highest-order interaction assumption fit into this framing. We present an approach to computation in the Bayesian setting which takes advantage of existing software and facilitates various sensitivity analyses. We demonstrate our approach in a case study of estimating the number of civilian casualties in the Kosovo war. Code used to produce this manuscript is available at https://github.com/aleshing/revisiting-identifying-assumptions.